Continuity mistake: In this movie, Emma Frost is seen as an adult woman [roughly around the same age as Professor X and Magneto]. But the character is also in X-Men Origins: Wolverine, set years later when Professor X and Magneto are much older, but in that movie she's younger than she is in this one. Although in Origins she is Kayla Silverfox's sister and her surname is never heard - the character was advertised and created as Emma Frost.
Continuity mistake: When Banshee is diving into the water, his "wings" are still attached. The shot angle changes, and his wings have disappeared before hitting the water. (01:39:20)
Continuity mistake: Before Shaw takes the grenade from Hendry, the latter one has his finger in the pin, and has it half pulled out by then. Look closely at Hendry's hand: he is still holding the pin, while Shaw takes the rest of the grenade, but in the next shot, Shaw pulls it out again. (00:28:10)
Continuity mistake: During the bar scene when the bartender is pouring beer for Eric, more than half of the glass is filled with foam (though it's in the background you can see it). But straightaway into the next shot when the bartender passes the beer to Eric, there is only a little amount of foam. (00:22:55)
Continuity mistake: The bartender points a gun at Erik, and his finger is inside the trigger guard. When Erik pushes the trigger using his superpower, suddenly the trigger guard is free of the finger. This is intentional, intended to illustrate the fact the Erik pushes the trigger, rather than the bartender pulling it. (00:24:40)
Continuity mistake: When Erik is first attempting to lift the submarine, he'd using his left hand. In subsequent scenes, specifically when Riptide turns into heavy wind to break Erik's grasp, he's now using his right hand.